Method for assigning a sample to one of multiple possible classes on the basis of experimental data

Abstract

The invention relates to a computer-implemented method for assigning a sample to one of multiple possible classes on the basis of experimental data of the sample, having the steps of: - receiving two-dimensional experimental data of the sample, the data comprising discrete values in a time dimension and discrete values in a further dimension; - ascertaining phase spectra by means of Fourier transformation of the received experimental data in the time dimension; and - assigning the sample to a class of the possible classes by ascertaining the Shannon entropy from the ascertained phase spectra. The invention further relates to a data processing device comprising means for carrying out the method according to the invention, and to a computer program product comprising instructions that, when the program is executed by a computer, cause the computer to carry out the above method, and to a computer-readable data carrier on which the above computer program product is stored.

Description

[0001] Ostwestfalen-Lippe University of Applied Sciences Düsseldorf, May 22, 2025 Our reference: UD 42389 / SAM ───────────────────────────────────────────────────────── Ostwestfalen-Lippe University of Applied Sciences Campusallee 12, 32657 Lemgo, Germany ─────────────────────────────────────────────────────────── Method for classifying a sample into one of several possible classes based on experimental data of the sample ──────────────────────────────────────────────────────── Description The invention relates to a computer-implemented method for classifying a sample into one of several possible classes based on experimental data. The invention also relates to a data processing device, a computer program, and a computer-readable data carrier. Currently, there is an effort to determine the sex of a future chick directly in the fertilized chicken egg.Different fluorophores are produced in male and female chicks during development within the bird egg. Due to their complex structure, the corresponding molecules exhibit unpredictable fluorescence. Fluorescence is the observed energetic transition from the excited state to the ground state of the molecule. This process is time-dependent. Document WO 2021 / 144420 A1 describes a device and a method for optical in-ovo sex determination in a fertilized bird egg. The device comprises a light source for emitting excitation radiation to stimulate fluorescence in a region inside the bird egg, a spectroscopic device for time- and / or spectrally resolved analysis of the fluorescence radiation emitted from this region inside the bird egg, and an evaluation unit for sex determination from the data obtained using the spectroscopic device.Furthermore, there is a desire to subject meat to cold storage for the purpose of meat maturation before marketing, in order to improve its tenderness and aroma. Currently, tenderness during the maturation process is determined destructively, for example, by a Warner-Bratzler shear force measurement. Based on this, the object of the invention is to provide means to increase the accuracy and / or improve the robustness of a method for classifying a sample based on two-dimensional spectroscopic data. In particular, the object of the invention is to increase the accuracy of in-ovo sex determination and / or improve the robustness of the method, as well as to enable the non-destructive determination of meat tenderness. According to the invention, this object is achieved by the features of the independent claim.Preferred embodiments of the invention are specified in the dependent claims, each of which, individually or in combination, can represent an aspect of the invention. According to the invention, a computer-implemented method for assigning a sample to one of several possible classes based on experimental data of the sample is provided, comprising the steps of: - receiving two-dimensional experimental data of the sample, wherein the data include discrete values ​​in one time dimension and discrete values ​​in another dimension; - determining phase spectra by Fourier transforming the received experimental data in the time dimension; and - assigning the sample to one of the possible classes by determining the Shannon entropy from the determined phase spectra. The data are discrete values ​​in the time dimension. In other words, they are individual experimentally determined measurements along a time axis.The additional dimension can encompass various forms, such as the frequency dimension or an electromagnetic wavelength, like the light or color dimension. This makes the method particularly versatile. To derive ^ from this two-dimensional data... ^ ^ ^ ^ To obtain the phase spectrum in the time dimension τ, a discrete Fourier transform is preferably performed. A discrete Fourier transform maps a time-discrete, finite signal that is periodically extended to a discrete, periodic frequency spectrum, which is also called the image domain. The signal ^^^^^ = ^^^^^, … , ^^^^^ = ^^^, … , ^^^ yields via the Fourier transform ^^^^^^^^ = ^^1^, … , ^^^^, where:^ Since the phase in this case is the information carrier, the imaginary Fourier coefficients yield the required phase spectra for ^ = 1, … , ^of ^ ^ ^^ ^ This approach simplifies the procedure, as the data to be processed is reduced to the minimum with the greatest information content. From these phase spectra, the Shannon entropy is preferably determined using the following formula with the probability p for the respective measured value: log ^#^^^(^^^^)^^ The Shannon entropy values ​​are thus ≥ 0. This means that the Shannon entropy represents the data to be analyzed in a single, easily manageable value. This also reduces the computational effort required. Therefore, the method is particularly well-suited for classifying a sample based on two-dimensional spectroscopic data, and it exhibits a particularly high success rate. In particular, the method achieves very high accuracy in in-ovo sex determination and allows for the non-destructive determination of meat tenderness. Furthermore, the invention relates to a data processing device comprising means for carrying out the above method. The invention also relates to a computer program product comprising instructions that, when executed by a computer, cause it to perform the above method.Furthermore, the invention relates to a computer-readable data carrier on which the above computer program product is stored. According to a preferred embodiment of the invention, the step of determining the phase spectra by means of a Fourier transform comprises a mathematical extension of the time dimension of the received data by at least one additional data point with a fixed value, wherein the Fourier transform is performed on the mathematically extended data in the time dimension. The Fourier transform is thus performed not only on the acquired two-dimensional data ^^^^^ = ^^^, … , ^^^, but also on mathematically extended signals ^-^^^^^^^ = ^0, ^^, … , ^^^, ^-^^^^^^^ =. mit at least one additional zero or with an additional arbitrary but fixed value at the coordinates 1, ... , ^ + 1, where 0 is preferred. These additional signals can minimize the effect of technical delay or biochemical variability of the sample. This is the case, for example, with measurement delay or different measurement times of the samples. According to a preferred embodiment of the invention, the step of determining the phase spectra by means of Fourier transform comprises a mathematical extension of the time dimension of the received data with zeros, i.e., data points with the value 0, up to a length of 2 mData points with m > 0, m ∈ ℕ. The zeros can be added at any position between, before, and / or after the signal values. The choice of the zero position(s) is adapted to the respective received data. From the resulting two-dimensional data ^^^^^ = ^^^, … , ^^^ a mathematically extended model with zeros such as ^1234^^^^ =^0, … ,0, ^ , … , ^ , 0, … ,0, ^ , … , , … ^ , … , ^ ^ the L m^ ^ 5^^^6 57^^6 ^ length of 2 data points to which the Fourier transform is applied. By adding zeros, a better classification accuracy of the two-dimensional data can be achieved without changing the content. According to a preferred embodiment of the invention, the step of determining the phase spectra by means of a Fourier transform comprises normalizing the received data in the time dimension such that a mean value of the data in the time dimension is zero, wherein the Fourier transform is performed on the normalized data in the time dimension. The obtained two-dimensional data ^ ^ ^ ^ ^are preferably in normalized form, where each individual value is normalized to the mean µ = 0 and the standard deviation : = 1. According to a preferred embodiment of the invention, the multiple possible classes, of which there are at least two possible classes, have complementary information contents. Due to the complementarity of the information contents of the data, the accuracy of the assignment can be significantly increased, since the presence of a specific class in data allows the conclusion that the other classes are excluded for this data. According to a preferred embodiment of the present invention, the two-dimensional experimental data are spectroscopic data with a time dimension and a wavelength dimension. The wavelength range preferably has subintervals with a bandwidth of up to ≥ 5 nm.According to a preferred embodiment of the invention, the sample is a fertilized bird egg, and the at least two classes represent a male and a female sex of the fertilized bird egg. The method has proven to be very suitable for determining the sex of the fertilized bird egg. It has been found that there are Shannon entropy values ​​to which only spectra of male bird eggs can be assigned, and there are values ​​to which only spectra of female bird eggs can be assigned. Entropy values ​​that occur in both sexes are not considered for this application. In particular, success rates of up to 100% have been achieved with the present method for assigning the sex of the fertilized bird egg. In a preferred embodiment, the fertilized bird eggs are examined up to the 5thThe eggs are examined spectroscopically on the day after fertilization. An examination up to the third day after fertilization is further preferred. Early determination of the sex of the fertilized bird eggs is particularly advantageous, as this makes the eggs available for their respective purposes at an early stage. According to a further preferred embodiment of the invention, the received two-dimensional spectroscopic data are autofluorescence data of the sample and, in particular, autofluorescence data of the sample, especially of the fertilized bird egg, acquired by means of time-resolved laser-induced fluorescence spectroscopy (zLIF) and / or time-correlated single-photon counting (TCSPC).Time-resolved laser-induced fluorescence spectroscopy (zLIF) and / or time-correlated single-photon counting (TCSPC) can be applied particularly easily and effectively to bird eggs, making the method readily scalable and enabling rapid sex determination of large quantities of eggs. For the detection of autofluorescence, spectroscopic data can be acquired using laser-induced fluorescence techniques. This method relies on the fluorescence excitation of the sample by an excitation pulse from a light source such as a laser or an LED. The fluorophores present in the sample, and preferably in the bird egg, are excited by the laser. After a certain time, typically on the order of a few nanoseconds to microseconds, the excited fluorophores will decay and emit light with a wavelength longer than the excitation wavelength.This fluorescence light is typically recorded with a photomultiplier tube (PMT) or a multichannel detector configured as an ICCD camera. In some methods—also known as boxcar methods—the complete spectrum is recorded at different times after each excitation pulse using an ICCD camera. Time-correlated single-photon counting (TCSPC) can also be used to detect the autofluorescence radiation. With TCSPC, the complete spectrum is not recorded after each excitation pulse. Instead, individual photons of a periodic light signal—in this case, the autofluorescence radiation—are detected, and the respective times between the excitation pulse of the pulsed excitation radiation and the arrival of the photon at the detection device are determined.In other words, the time measurement is started by the excitation pulse, and the photon emitted during the transition from the excited state to the ground state stops the measurement. The measurement is repeated many times, and the individual time-correlated photons, relative to the excitation pulse, are sorted into a so-called TCSPC histogram according to their measured time. The TCSPC histogram represents the time course of the autofluorescence radiation after excitation. Preferably, the TCSPC histogram generated by the detection device has a bin width, also called the class width, for histogram classes from 1 ps to 50 ps, ​​preferably from 10 ps to 20 ps. Preferably, the bin width of the TCSPC histogram can be adapted to the device and / or the sample under investigation.Furthermore, when adjusting the class width of the TCSPC histogram, a temporal resolution of the entire device – and particularly preferably a full width at half maximum (FWHM) of the instrument response function (IRF) – is preferably taken into account. The FWHM of the IRF depends essentially on the light source and a pulse length generated by the light source and / or on a detector element of the detection device.According to a further preferred embodiment of the invention, at least one of the steps of the method, namely receiving the two-dimensional experimental data of the sample, determining phase spectra by means of Fourier transformation of the received experimental data in the time dimension, and / or assigning the sample to a class of possible classes by determining the Shannon entropy from the determined phase spectra with data comprising at least one of the wavelength ranges 410 nm to 425 nm, 455 nm to 465 nm, 465 nm to 480 nm, 505 nm to 540 nm, 535 nm to 550 nm, 575 nm to 595 nm, 615 nm to 630 nm, 660 nm to 670 nm, and / or 715 nm to 730 nm, is carried out. These ranges have proven to be particularly suitable for determining the sex of the fertilized bird egg with a very high success rate.By requiring only the measurement and / or processing of portions of the spectra, the method is simplified and can be performed more quickly. According to a further preferred embodiment of the invention, the step of assigning the sample to a class of possible classes by determining the Shannon entropy from the determined phase spectra comprises the following steps: identifying clusters using cluster analysis based on the determined Shannon entropy, identifying trend components of the identified clusters, and calculating a trend function based on the identified trend components. Cluster analysis is used when it is still unknown which areas of the data contain the desired information. Cluster analysis is generally used to identify similarity structures in large datasets.The groups of similarity structures found in this way are called clusters, and the process is called clustering. Once these clusters containing the desired information have been identified, the relevant trend components can be determined, forming the basis for the trend function. Using the trend function, new data can then be automatically assigned to the clusters and thus to a class of possible classes. In a preferred further development, the two-dimensional experimental data are two-dimensional vibroacoustic data with a time dimension and an amplitude dimension. Such data are easily accessible experimentally because they can be obtained non-destructively. Vibroacoustic measurements provide a time series signal. 7 ;^ ^ for a test j on days d=0, 1, ...: The two-day time series signal ^ 7 ; > ^ ^ and ^ 7 ; ?^ ^ (or several days) is a corresponding composite signal made up of Die The values ​​of this vector are measurements at times t1, ⋯, t n Preferably, the discrete Fourier transform is then used to convert the signal ^ 7 ; ^ ^ from the time domain into a signal of the same length into the frequency domain. The elements ^^7 7; ^1^, ⋯ , ^; ^^^^ are defined as follows: Each element ^7; ^^^, as the sum of all ^;^ ^^, ^ = 1, … , contains contributions from each individual ^ ; ^ ^ ^. It follows that elements in the frequency domain can have a higher entropy than those in the original time domain. In the formula above, i 2 = -1, therefore all Werte ^7; ^^^ = E^%^7; ^^^& + $ ^^%^7; ^^^& complex numbers. For simplification, it is preferably defined as follows: ℱ7; ^^^ ∶= ℱ7 7; @^;^ ^A. Trend extrapolation is a construction of a trend function GH32I: ℝ;×^ → ℝ, in this case in the frequency domain, with the following property to be investigated: G ⋯ ℱ7^^^^ ≈ 7 Trend extrapolation preferably provides the desired property value for any arbitrary sample j in a first step. The Shannon entropy is then calculated from the resulting phase spectrum: ^ ∙log @#^^^%^; ^^^&^A In the second step, trend components are determined for the individual clusters: The trend component is the real part of the Fourier transform E^%^ 7 ;^^ U ^&, which is defined by a coefficient ^U that has the greatest influence on the prediction of the class. From this, a linear trend function is finally calculated as: G H32I^E^%^7; ^^U^&^ = T ∙ E^%^7; ^^U^& + V where a and b are parameters from the linear trend fit to all samples. The quality of the fit is represented by the Pearson correlation coefficient ρ: where W ∈ (−1,1), R"X denotes the statistical covariance and σ the variance; for a perfect fit, ρ=1, which signifies a fitting accuracy of 100%. According to a further preferred development of the method, meat from slaughtered animals is used as the sample, in particular muscle meat, and the possible classes (P1, P2, P3) are used. n) represent the tenderness of the meat. According to a further preferred embodiment of the method, in cluster analysis, zero-point completion can also be considered as a day-separating element in a signal composed over several days. This can further increase the accuracy. Further technical advantages and effects of the method for assigning a sample to one of several possible classes based on experimental data, the data processing device, the computer program product, and the computer-readable data carrier will become apparent to those skilled in the art from the embodiments described below. The invention is explained in more detail below with reference to the drawings. The illustrated embodiments are highly schematic, i.e.,The distances and the lateral and vertical dimensions are not to scale and, unless otherwise stated, do not exhibit any derivable geometric relationships to each other. In the drawing, Fig. 1 shows a schematic representation of two-dimensional spectroscopic data of a sample, which are obtained within the framework of the method for classifying a sample into one of several possible classes based on experimental data of the sample according to a preferred embodiment of the invention; Fig. 2 schematically shows the result of a cluster analysis carried out within the framework of the method according to a preferred embodiment; and Fig. 3 shows a trend function based on the determined trend components, which was found within the framework of the method according to a preferred embodiment.In a first embodiment, the measured spectroscopic data are time-resolved fluorescence emissions measured on bird eggs on the third day of incubation. The sex of the eggs was determined by PCR. Such data are schematically represented in Figure 1, showing the decay curve for a single wavelength 10a and an averaged decay curve over the wavelength range 10b. The y-axis 12 represents the fluorescence intensity and the x-axis 14 represents time τ. The emission ranges are empirically decomposed into sub-intervals, each 5 nm wide. The decomposition into these sub-intervals, i.e., by increasing or decreasing the interval boundary, can be varied. Three clusters of data always result for each sub-interval: male, female, and indifferent. During classification, the entropy values ​​are uniquely assigned to the male and female classes and then tested.The system is trained using machine learning with 80% of the spectra for each sex and then tested with the remaining spectra. The most productive ranges for female bird eggs are, for example, 410 nm to 425 nm, 455 nm to 465 nm, and 660 nm to 670 nm. Within these ranges, all existing female spectra are clearly identifiable. The following table shows examples of entropy values ​​from the 410 nm range that are "purely" female and "purely" male and occur in both sexes: female male indifferent 1.3710 1.2917 0.3534 1.4299 1.4295 0.6998 1.7534 1.6049 0.7219 1.7819 1.7232 0.8366 1.7968 1.7274 0.9056 Furthermore, a modeling approach with more than one additional and, for example, periodically continued zero is also possible, such that at least one signal value lies between two zeros.This can further improve accuracy through lower misclassification rates and higher yield in the individual areas. Furthermore, various strategies for adding zeros during modeling are possible with n signal values: 1. An equal number of zeros before and after the signal values ​​(up to a difference of 1, if the original number of signal values ​​is odd (n is odd) or if there are zeros between the signal values); 2. A single zero between the signal values; 3. Periodically distributed zeros between the signal values; 4. The maximum possible number of zeros between the signal values ​​(number of zeros = n - 1); 5. The second- or third-largest maximum possible number of zeros between the signal values ​​(number of zeros = n - 2 or n - 3, respectively).These strategies offer advantages such as: Strategy 1 is particularly suitable for increasing the signal resolution. Strategy 2, as well as periodic distributions of zeros as in Strategy 3, are particularly well-suited for two-dimensional wavelength data. Strategies 4 and 5 are especially advantageous for increasing data variability. These strategies are not exhaustive and merely represent possible examples that can also be combined. When applying strategies to unknown datasets, each position that does not contain a signal value can be assigned a zero. This limits the data points to a specific length of 2. mData points with m > 0, m ∈ ℕ are filled, and the best strategy for all possible combinations is determined through empirical trials. It has been found that for assigning the sex of bird eggs, augmenting the signal values ​​with zeros to a length of 512 is particularly advantageous. The number of added zeros is adjusted to the number of data points for each subsequent length of 2. mData points (e.g., for 30 data points, the number is padded to 64). In another preferred embodiment, the method is used to determine the tenderness of meat. Tenderness is the property under investigation. The data are presented as examples without normalization or standardization and without zeroing. The evaluation is suitable for clustering and subsequent trend analysis or regression analysis. The beef maturation process from day 0 to day 21 and the achieved tenderness were analyzed using a non-destructive vibroacoustic measurement system on 30 samples. The samples came from cattle of different breeds, at least 5 breeds in this case. The system was trained on 25 samples using machine learning and subsequently tested on 5 samples. As a reference, tenderness was determined destructively by Warner-Bratzler shear force measurement and sensory evaluation with human subjects.The samples were measured daily for d = 21 days. For example, empirical measurements were taken for n = 9 samples, with t1 = 5 sec at equidistant intervals up to t5 = 65 sec, and t6 = 3 min, t7 = 3 min 15 sec, and t8 = 6 min, t9 = 6 min 15 sec. In the first step, measurements from days 2 to 3, identified as the days of the most intensive ripening process, were used. This step resulted in a subdivision of the samples into characteristic clusters: lower entropy values ​​at 1.2, medium entropy values ​​between 1.6 and 1.8, and high entropy values ​​greater than 2. Medium to high entropy values ​​are expected for delicate samples. This step is illustrated in Figure 2, where the Shannon entropy is plotted on the y-axis (12) and the trend components on the x-axis (14). The samples are assigned to the high-fragility cluster 18 and the low-fragility cluster 20. Furthermore, the samples used are numbered from 1 to 23 in Figure 2.After the second step, in which the trend components are determined, the tenderness on the scale from 20 = very tender to 80 = not tender can already be predicted on day 4. This is shown in Figure 3, where the y-axis (12) represents tenderness and the x-axis (14) represents the trend components for samples with medium entropy. From days 0 to 4, the tenderness of the samples with medium entropy is predicted by the linear trend function with a fit accuracy of approximately 82%. The average deviation is 7.43, and the maximum deviation is 22.23. The achieved correlation coefficient of samples from the high-entropy cluster and the trend function is 81.5%. The average deviation is 3.18, and the maximum deviation is 5.36. The results for the 5 test samples: Sample No. Entropy Cluster Delicacy (determined) Delicacy (precedented) Difference 26 2.0588 to the power of 53 36.7 16.3 27 2.0588 to the power of 49 48.8 0.2 28 1.6577 average 49 33.6 15.4 29 1.6577 average 50 24.2 25.8 30 1.6577 average 54 54.5 0.5 The data show that the value obtained from the trend function correlates with the predicted fragility. As with sex determination, normalization or standardization as well as zero-filling can be applied here, which can lead to even more precise predictions.

[0002] Reference symbol 10a Decay curve for singular wavelength 10b Averaged decay curve over wavelength range 12 y-axis 14 x-axis 16 Wavelength range 18 Sample with high sensitivity 20 Sample with low sensitivity

Claims

Patent claims 1. Computer-implemented method for classifying a sample into one of several possible classes based on experimental data of the sample, comprising the steps of: - Receiving two-dimensional experimental data of the sample, wherein the data include discrete values ​​in one time dimension and discrete values ​​in another dimension, - Determining phase spectra by Fourier transforming the received experimental data in the time dimension, and - Assigning the sample to one of the possible classes by determining the Shannon entropy from the determined phase spectra. 2.A method according to claim 1, wherein the step of determining the phase spectra by means of a Fourier transform comprises mathematically extending the time dimension of the received data by at least one additional data point with a fixed value, preferably with zeros, and performing the Fourier transform on the mathematically extended data in the time dimension.

3. A method according to any one of the preceding claims, wherein the step of determining the phase spectra by means of a Fourier transform comprises normalizing the received data in the time dimension such that the mean value of the data in the time dimension is zero, and performing the Fourier transform on the normalized data in the time dimension.

4. A method according to any one of the preceding claims, wherein the multiple possible classes are at least two possible classes that have complementary information contents. 5.Method according to one of the preceding claims, wherein the two-dimensional experimental data are two-dimensional spectroscopic data with a time dimension and a wavelength dimension.

6. A method according to any one of the preceding claims, wherein the sample is a fertilized bird egg and the two classes represent a male and a female sex of the fertilized bird egg.

7. A method according to claim 6, wherein the bird eggs are spectroscopically examined up to the 5th day after fertilization.

8. A method according to any one of the preceding claims, wherein the received two-dimensional experimental data are intrinsic fluorescence data of the sample and, in particular, intrinsic fluorescence data of the sample acquired by time-resolved laser-induced fluorescence spectroscopy (zLIF) and / or by time-correlated single-photon counting (TCSPC). 9.A method according to any one of claims 5 to 8, wherein at least one of the steps is performed: receiving the two-dimensional experimental data of the sample; determining phase spectra by Fourier transformation of the received experimental data in the time dimension; or assigning the sample to a class of the possible classes by determining the Shannon entropy from the determined phase spectra, with data comprising at least one of the wavelength ranges 410 nm to 425 nm, 455 nm to 465 nm, 465 nm to 480 nm, 505 nm to 540 nm, 535 nm to 550 nm, 575 nm to 595 nm, 615 nm to 630 nm, 660 nm to 670 nm, and / or 715 nm to 730 nm.Method according to one of claims 1 to 3, wherein the step of assigning the sample to a class of the possible classes by determining the Shannon entropy from the determined phase spectra comprises the steps of - determining clusters by means of a cluster analysis on the determined Shannon entropy, - determining trend components of the determined clusters and - calculating a trend function based on the determined trend components.

11. A method according to any one of claims 1 to 3 or 10, wherein the two-dimensional experimental data are two-dimensional vibroacoustic data with a time dimension and an amplitude dimension.

12. A method according to any one of claims 1 to 3 or 10 to 11, wherein the sample is meat from slaughtered animals, in particular muscle meat, and the possible classes represent the tenderness of the meat.

13. A data processing device comprising means for carrying out the method according to any one of the preceding method claims.

14. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to any one of the preceding method claims.

15. A computer-readable data carrier on which the computer program product according to the preceding claim is stored.

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